Linear Interpolation

Box filter is simple and well known technique for image resizing. This technical paper describes an algorithm for image downscaling (shrinking) using box filter with subpixel accuracy, based on color space rescaling, which avoids oating point arithmetics. All operations in accompaniment C++ code are completely integer based, which signicantly improves image shrinking speed and quality.

To alleviate the feed fluctuation and to maintain a smooth feed in conventional five-axis machining, an optimal feed interpolation algorithm (look-ahead) is proposed. However, the problem arises where the segment usually cannot be interpolated exactly in an integer period because of the nonzero joint feed at the junction. To overcome this problem, and to achieve faster machining speed and higher quality parts, this paper presents an optimal feed interpolation algorithm for high-speed, five-axis machining having the function of “look-ahead”, i.e., variable-period linear interpolation algorithm. In real applications, the proposed algorithm results in: (1) constant speed; (2) high machining accuracy. Moreover, in this paper, an efficient method for acceleration and deceleration control is presented to achieve the highest-quality feed profiles and to shorten machining times. The precision and speed of machining is improved greatly. Experimental results verify the effectiveness of the proposed method.

The purpose of this experiment is two-fold: 1. To demonstrate how a common data analysis procedure – interpolation – can be implemented in Azure Machine Learning Studio (Azure MLS) and 2. To show how the use of R can extend capabilities of the Azure MLS.
Botchkarev, A. (2018). Data Analysis and Interpolation Using R. Experiment in Microsoft Azure Machine Learning Studio. Azure AI Gallery. https://gallery.azure.ai/Experiment/Data-Analysis-and-Interpolation-Using-R The purpose of this experiment is to demonstrate how interpolation can be implemented in Azure MLS using R.

This paper presents a full-discretization method based on the direct integration scheme for prediction of milling stability. The fundamental mathematical model of the dynamic milling process considering the regenerative effect is expressed as a linear time periodic system with a single discrete time delay, and the response of the system is calculated via the direct integration scheme with the help of discretizing the time period. Then, the Duhamel term of the response is solved using the full-discretization method. In each small time interval, the involved system state, time-periodic and time delay items are simultaneously approximated by means of linear interpolation. After obtaining the discrete map of the state transition on one time interval, a closed form expression for the transition matrix of the system is constructed. The milling stability is then predicted based on Floquet theory. The effectiveness of the algorithm is demonstrated by using the benchmark examples for one and two degrees of freedom milling models. It is shown that the proposed method has high computational efficiency without loss of any numerical precision. The code of the algorithm is also attached in the appendix.

The present article discusses various preprocessing techniques suitable for dealing with time series data for environmental science-related studies. The errors or noises due to electronic sensor fault, fault in the communication channel, etc., are considered here. Such errors or glitches that occur during the data acquisition or transmission phases need to be eliminated before it fed to the forecasting or classification systems. Computationally simple and efficient techniques are discussed here so that they can even be adopted for a hard real-time system environment. While adopting these techniques, we may also end up with some of the real genuine values, which may consider as an outlier. A special indicator function, the moving Inter Quartile Range (MIQR) algorithm, is proposed to overcome such special cases.

This paper presents a method, which the author proposes to call Percentage Correlation Technique, for interpolating a curve between two known curves, which have a direct relationship to a second set of curves, whose functions are known. Although, the method itself is a variation of linear interpolation technique, the curve functions of all curves can be either linear or non-linear. It is shown how this method is applied in a real world application of calculating electrical contact resistance of digital interconnect socket pins.

Abstract Second-order accurate projection methods for simulating time-dependent incompressible flows on cell-centred grids substantially belong to the class either of exact or approximate projections. In the exact method, the continuity constraint can be satisfied to machine-accuracy but the divergence and Laplacian operators show a four-dimension nullspace therefore spurious oscillating solutions can be introduced. In the approximate method, the continuity constraint is relaxed, the continuity equation being satisfied up to ...

In this paper, the linear interpolation technique is applied to reconstruct the reflectance curves of the Munsell color chips from their tristimulus color coordinates. Interpolation method has been applied by using a look-up table (LUT) for transforming color values from the color space to the second multi-dimensional spectrophotometric domain. Tristimulus values of Munsell color chips have been used for creating the look-up table. Results of recovery are evaluated by the metamerism index under two different standard light sources and the root mean square (RMS) error. The results showed that the metamerism indices between the actual and the reconstructed curves were totally small. The negligible values of the RMS error also indicate the suitability of the proposed method. J. Color Sci. Tech. 2(2008), 1-7. © Institute for Colorants, Paint and Coatings. Keyword: Reflectance curve, Interpolation, Reconstruction, Tristimulus value.

Polar ordination is used to project all pixels in Landsat TM band space onto a single axis whose endpoints are the centroids of training areas in two spectrally distinct natural forest types - one with and the other without bamboo - which dominate the landscape in the southwest Amazon. Assuming the same wood density in both forests, biometric data collected in the training areas (Oliveira, 2000) indicated that biomass of forest with high bamboo density was 29% lower than forest without bamboo. Linear interpolation along the ordination axis models biomass of spectrally intermediate pixels. Thresholds based on band-space distance from the axis and ordinated distance beyond the axis endpoints are used to mask pixels unacceptable for modeling: water, beaches, pastures, roads, urban area, and deep topographic shade. The final product is a biomass image of an area covering 90x90 km, with 79% of all pixels being modeled. Because of spectral variability between bamboo forests in different r...